As we have presented in the introduction, direct numerical simulations must be capable of predicting the developing two-phase fluid interfacial dynamics featuring interface breakup, and droplet coalescence. In light of this,
we aim to show the capabilities of our numerical framework in the prediction of the scaling laws for the capillary singularity of liquid threads.
As the point of singularity approaches, the system is driven locally by the large interfacial curvature, and its interfacial dynamics depends solely upon the physical properties of the liquid. [1]} have suggested that the pinchoff of a viscous thread (of radius \(r(z,t)\) , density \(\rho \) , viscosity \(\mu \)  and surface tension \(\sigma \) ) surrounded by another viscous fluid transits between different dynamical regimes as \(r(t) \rightarrow 0\)  towards the breakup time \(\tau \)  (see figure 1 of [1]}). The thinning of a water thread, surrounded by air, transitions from an inertial-capillary regime (\(r\sim \tau ^{2/3} \)  and \(u\sim \tau ^{-1/3}\)  ) to an inertial-viscous regime (\(r\sim \tau \)  and \(u\sim \tau ^{-1/2}\)  ), more details can be found in [3]}, [4]} and [1]}.
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